Complexity and Finding the Right Path

by Jon N. Hall8/26/14
In June 2011 at American Thinker, I wrote a blog to alert folks to an HBO special: Bobby Fischer Against the World. The reason I thought AT readers might like the film is because of its historical and political elements. Also, it dealt with Fischer the man, and his descent into madness. The blog is very short, and you might click on the link just to see the before-and-after photos I provided. They show the young Fischer looking like a fashion model with an attitude and the older Fischer looking like some demented hobo.

In any event, in that little blog I did briefly comment on Bobby’s game: “Chess is probably a ruined sport anyway, as computers have bested carbon-based life forms. What need is there for creativity and genius when there’s the brute force of gigahertz and terabytes?”

By “ruined sport,” what I was probably vaguely thinking about is that a computer program could be written that would “play” all possible “games.” The program would play every possible variation, make every possible move, and then put it all in a giant array. When the program had gone as far as it could go in each variation, it would backtrack one move, record whether there had been a checkmate for white or for black, and then take the next branch, and so on and so forth until all possibilities had been exhausted. The program would have no strategy; indeed, no intelligence. It would just mindlessly go down each path as far as it could.

So a computer playing chess against a carbon-based life form like a human would merely be looking up already-played games whose outcomes were already “on file.” The computer would “know” that such and such a move results in x number of checkmates for white and y number of checkmates for black. The “brute force” would be in creating the array.

But now that I’ve thought about it, this idea seems quite dumb. For one thing, the array of games would be bigger than you can imagine. The time it would take the fastest super-computer to play all possible games and record them makes the run time unfeasible, (I don’t even want to think about the electricity bill). But here’s the big reason why this is a dumb idea: Way, way more than 99.9 percent of the recorded games would be … dumb.

I just now made up that statistic, but I think it is right. Except for the threefold repetition rule and the fifty-move rule, there’s nothing in the rules of chess to prevent moving the same piece back and forth over and over again. Those idiotic moves would all be recorded. So the “brute force” strategy I’ve outlined would create an array that would consist almost entirely of garbage games. But here’s the deal breaker, some of the really dumb “games” might result in checkmate. So a computer playing against a human couldn’t just look up how many checkmates a move results in for one side versus the other; the computer would need to assess the “quality” of the checkmates; e.g. a checkmate that resulted after 40 moves would be of a higher “quality” than one that resulted after, say, 4,000. (The longest tournament game in history lasted 269 moves.)

Chess is a game of labyrinthine complexity. For the first move, there are 20 possibilities. Even I can figure out that after both sides have taken their first move, that there are 400 possible positions. From there it gets really hairy; indeed, exponentially so. To find out what those exponents might be, read this short blog: “How many different ways can a chess game unfold?”

What I was aiming at with my huge array of all possible games was to get around the complexity in chess; chess would be “ruined” because all outcomes would be “on file.” The above blog estimates that there are more than a googol “typical” games; those of about 40 moves. But if the blog’s numbers for all possible games are anywhere near to being correct, then my idea is a nonstarter; creating the array would be impossible.

I don’t know how the computers that have been beating humans are programmed. But I do know that chess involves strategy, tactics, judgment, creativity, and even intuition. And those things have got to be much, much more difficult to program than my dumb array.

Bobby Fischer has been called “the Mozart of chess.” High praise, that. (I’m a Mahlerite, and Mahler’s Last Words were: “Mozart.”) I recorded the HBO flick on Fischer and had meant to screen it again, but my bundler’s DVR crapped out on me (and not for the only time). Anyway, as I recall the flick touched on Game 6 of the Fischer-Spassky championship in 1972, which ended after Fischer’s 41st move with Spassky resigning. Some have compared the Sixth Game to a Mozart symphony.

In the film Amadeus (1984), after a performance of a new work, Mozart asks Emperor Joseph if he liked it. After some hemming and hawing, the emperor tells Mozart that there are “too many notes”:

MOZART: I don’t understand. There are just as many notes, Majesty, as are required. Neither more nor less.

EMPEROR: My dear fellow, there are in fact only so many notes the ear can hear in the course of an evening. I think I’m right in saying that, aren’t I, Court Composer?

SALIERI: Yes! yes!, on the whole, yes, Majesty.

MOZART: But this is absurd!

EMPEROR: My dear, young man, don’t take it too hard. Your work is ingenious. It’s quality work. And there are simply too many notes, that’s all. Cut a few and it will be perfect.

MOZART: Which few did you have in mind, Majesty?

Great dialog, no? Here’s a short video of this witty scene. And here’s the wonderful video of the scene wherein Salieri says of Mozart: “Replace one note, and there would be diminishment. Replace one phrase, and the structure would fall.” (Clearly, the emperor needed music lessons.)

There is a type of beauty that is associated with simplicity; it is called “elegance.” Both Fischer and Mozart could achieve such beauty. What elegance reveals are the essential relations between things. “Elegance” also describes mathematical beauty. Elegance is attained with the fewest possible elements: neither more nor fewer notes than the master requires for his aria; neither more nor fewer moves than the grandmaster needs for checkmate. The enemy of elegance is complexity.

It’s not difficult to make something complex; just add more elements. When I moved off-campus in college, I started cooking. And I had this crazy idea that adding more and more herbs and spices would make my oeuvres more interesting. But I learned that fewer elements can be tastier.

Complexity is why ObamaCare, the Federal Register, and the federal income tax code are all so damned ugly. But there was never a chance that such laws could have been otherwise, given who created them.

Complexity is the first refuge of simple people. The superior mind seeks to make the complex simple; another sort of mind seeks to make the simple complex. That last sort of mind is often defective. Puny intellects endeavor to bolster their reputations with claims of “complexity”; even dropping the word “complexity” is supposed to garner one points. On May 9 on The McLaughlin Group, Eleanor Clift said:

Every media organization has investigated this to death. This animates the right wing of the Republican Party. And I would like to point out that Ambassador Stevens was not murdered. He died of smoke inhalation in the safe room in the CIA installation.

The pathetic idea that Stevens wasn’t murdered, which lawyers would tear apart with ease, isn’t what interests me. Rather, it’s what Clift said later on in doubling down on her inanity that’s really amusing: “I was just trying to add a little bit of complexity, and I’m going to stick with what I said. I realize this causes a lot of emotion.” (Right … you go, girl.)

In “Going the Distance,” a January 2014 article in The New Yorker of about 16,648 words covering 18 pages, David Remnick writes: “This is the archetypal Obama habit of mind and politics, the calm, professorial immersion in complexity played out in front of ardent supporters who crave a rallying cry.” The only other iteration of “complexity” in the article comes from the president himself: “I am comfortable with complexity.”

And that’s why it takes Obama so long to make decisions. You see, he’s taking everything into account; he’s going down every path, playing every variation, just like my computer program. And while he’s off thinking about everything in all its sublime complexity, America continues to decline.

4 Responses to Complexity and Finding the Right Path

Of course Stevens wasn’t murdered; neither was James A. Garfield. (He died as a result of infection from the doctors’ attempt to locate the bullet Charles Guiteau fired into him. For some strange reason, the jury rejected Guiteau’s argument. Too bad for him Eleanor Clift wasn’t a member.)

The Curious Journal has a weekly chess puzzle, which I try to solve (and sometimes succeed).

An interesting suggestion as to what happened to Fischer can be found at the end of Fritz Leiber’s short story “Midnight by the Morphy Watch”.

Actually, the reason why it takes Obama so long to make decisions is that he doesn’t know what to do – he’s completely incompetent. Even given his malicious intent of harming this country by turning it into a weak, decadent Euro-style social democracy headed toward dictatorship, Obama still has trouble deciding which course will achieve that end without bringing political disaster down upon himself. This is especially true in foreign policy, which Obama doesn’t really care about except to make the U.S. less important in the world and to help out the Muslim Brotherhood where he can.

As for chess, I don’t worry about it too much. Jon might be interested in an old article by Mikhail Botvinnik, published probably in Chess Review during the late-50’s, in which Botvinnik (chess champion and engineer) explained how computers (then in their infancy) approach chess by calculating all the possible consequences of every move. I remember seeing this article reprinted in book form during the 60’s. Botvinnik said that because there were so many possible moves, the computer could not possibly calculate all of them because each computation took a fair amount of time. Of course what Botvinnik could not foresee was the advent of the supercomputer with its unbelievable speed of calculation. It was fairly obvious by the late-70’s that sooner or later, a computer that could defeat a human being at chess would be feasible.

As I say, for myself I don’t worry about this, although the idea of a machine doing something a man can’t has been disturbing people for a long time, quite needlessly in my view (see the legend of John Henry). Chess is not music and Bobby Fischer is not Mozart, and in the end it no more should bother us that a machine can outplay a man than it should that a computer can multiply two numbers more quickly, or that a bulldozer can move far more earth in an hour than a man can. Computers still can’t think as we do, and perhaps the naive hopes of the artificial intelligence crowd would make a good subject for another article by Jon.

People have often been optimistic about the limits of computers. Even the early ones were more powerful than anticipated, as the Germans eventually found out when they learned how their “unbreakable” Enigma cipher was regularly read by the British.

Would it be a “ruined sport” if someone designed a robot that could always win Wimbledon? This is what I’ve never understood about this entire controversy. Yes, a machine can be programmed to do remarkable things these days. And let machines play machines. But why should we lose one minute of sleep over the fact that an electronic device — which are especially good at doing billions of instructions per second — can beat a human at chess?

Let humans play humans and computers play computer. And if a human wants to play a computer, fine. But it’s clear now that via brute-force that a machine can win at chess. And should we ever produce a robot nimble enough to beat the best at tennis, that will be a remarkable thing in terms of the advancement of robotics. But no one should then suppose that we must re-order the sports world (or our view of human achievement) to accommodate what silicon can do.